| 释义 |
hypercycle, n. Math.|ˈhaɪpəsaɪk(ə)l|
[In sense 1, a. F. hypercycle (E. N. Laguerre 1882, in Compt. Rend. XCIV. 779): cf. hyper-, cycle n. Sense 2 was coined independently in Eng.]
1. a. (Formerly at hyper- IV.) Any of a class of sextic curves to which the line at infinity is a double tangent. Now rare.
1889in Cent. Dict. s.v., Hypercycle, a plane curve of the sixth order and fourth class having the line at infinity as a double tangent, which possesses the property that two pairs of tangents to it may be so taken that, whatever fifth tangent be considered, the two circles inscribed or escribed in the two triangles formed each with one of the pairs of fixed tangents and the variable tangent have their points of contact with the latter at a constant distance.
b. In Lobachevskian geometry, a curve consisting of all points at the same perpendicular distance from a particular straight line.
1909in Cent. Dict. Suppl. s.v., Hypercycle, n. 2. Same as equidistantial. 1942H. S. M. Coxeter Non-Euclidean Geom. xi. 213 Some authors use the distinctive word cycle for the general circle in hyperbolic geometry, and distinguish the three kinds as a circle, a horocycle, and a hypercycle. 1981Sci. Amer. Oct. 16/3 The lines are called equidistant curves or hypercycles.
2. In mathematical biology, a system of self-replicating molecules each of which reproduces itself only when catalysed as a result of the replication of another molecule in the system, the whole being considered as a possible intermediate stage in the development of spontaneously self-replicating molecules.
1971M. Eigen in Naturwissenschaften LVIII. 504/1 The system represents a ‘cyclic hierarchy’ in which many cyclic (complementary) nucleotide collectives are linked together by an enzymic ‘hyper-cycle’. 1981Bio Systems XIII. 235 The notion of hypercycles has been introduced..in order to characterize a functional entity which integrates information stored in individual self-replicating elements. 1986Jrnl. Theoret. Biol. CXVIII. 9 From the study made so far we come to a conclusion that a catalytic hypercycle evolves into a more complex and organized one by a succession of alternate instability and stability. |